Best Known (7, ∞, s)-Nets in Base 64
(7, ∞, 177)-Net over F64 — Constructive and digital
Digital (7, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
(7, ∞, 520)-Net in Base 64 — Upper bound on s
There is no (7, m, 521)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (7, 519, 521)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64519, 521, S64, 512), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1635 258712 244846 415110 017884 053326 903987 427045 254264 734963 155812 144278 118329 337111 514253 610020 486718 949953 051045 853796 993538 250266 526983 294146 381551 962048 492845 483697 003567 315884 777138 696463 973933 425315 829279 859064 172145 585679 967799 727563 454564 166663 693031 330612 863094 566262 035530 387015 937458 487704 766093 423733 168107 359269 178511 017666 339929 584211 525087 231203 525479 478158 322388 289940 524613 922972 384520 202283 940854 266086 885759 515996 384879 466247 662867 957175 664459 520191 923299 255737 047833 713416 378744 388521 875112 646037 037726 289524 125546 946742 581787 051089 044413 378516 875418 963370 931033 989261 502371 204616 679841 549213 772730 022356 657778 477955 109972 702720 326264 936952 242858 585464 832965 721132 231982 605227 865079 257824 963041 888567 631080 631405 501216 368017 539853 947111 472328 014381 078431 746509 604387 476025 600433 961049 784388 455411 773535 440626 273902 828766 386553 492492 620893 873100 348937 732823 712102 600191 839891 953180 550326 728953 545326 074084 227417 202099 224576 / 57 > 64519 [i]
- extracting embedded OOA [i] would yield OA(64519, 521, S64, 512), but